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The nested parallel (a.k.a. fork-join) model is widely used for writing parallel programs. However, the two composition constructs, i.e. "$\parallel$" (parallel) and "$;$" (serial), are insufficient in expressing "partial dependencies" or…
This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…
It is a notable trend to use Large Language Models (LLMs) to tackle complex tasks, e.g., tasks that require a sequence of actions and dynamic interaction with tools and external environments. In this paper, we propose StateFlow, a novel…
In this work we present a clustering technique called \textit{multi-level conformal clustering (MLCC)}. The technique is hierarchical in nature because it can be performed at multiple significance levels which yields greater insight into…
The application of formal methods to the analysis of stochastic oscillators has been at the focus of several research works in recent times. In this paper we provide insights on the application of an expressive temporal logic formalism,…
The paper studies sequential reasoning over graph-structured data, which stands as a fundamental task in various trending fields like automated math problem solving and neural graph algorithm learning, attracting a lot of research interest.…
In this paper we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
This paper describes an open-source Python framework for handling datasets for music processing tasks, built with the aim of improving the reproducibility of research projects in music computing and assessing the generalization abilities of…
This paper introduces the Token Space framework, a novel mathematical construct designed to enhance the interpretability and effectiveness of deep learning models through the application of category theory. By establishing a categorical…
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
Nowadays, numerous services based on large-scale distributed systems have been developed to boost the convenience of human life. On the other side, it becomes a significant challenge to ensure the correctness and properties of these systems…
This paper is about a categorical approach to model a very simple Semantically Linear lambda calculus, named Sll-calculus. This is a core calculus underlying the programming language SlPCF. In particular, in this work, we introduce the…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Knowledge graphs have emerged as a widely adopted medium for storing relational data, making methods for automatically reasoning with them highly desirable. In this paper, we present a novel approach for inducing a hierarchy of subject…
We propose a framework for a global description of the dynamics of complex flows via clusterized spatial representations of the flow, isolating and identifying local dynamics, retrieving different Space-Time Cluster-Based Network Models…